Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-12-26
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
We consider the cluster and backbone mass distributions between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold $p_c$. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, $\theta$. The fractal dimensions of both the cluster and backbone mass are independent of w, r, and $\theta$. The slope of the power law regime of the cluster mass is unaffected by changes in these three variables. However, the slope of the power law regime of the backbone mass distribution is dependent upon $\theta$. The characteristic mass of the cluster also depends upon $\theta$, but the characteristic backbone mass is only weakly affected by $\theta$. We propose new scaling functions that reproduce the $\theta$ dependence of the characteristic mass found in the simulations.
Baker Don R.
da Silva Luciano R.
Havlin Shlomo
Paul Gerald
Stanley Eugene H.
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